{"id":"cb_question_bank:98b85f4b-3df7-4134-ad99-0b24b83bf7f6","source_id":"cb_question_bank","source_item_id":"98b85f4b-3df7-4134-ad99-0b24b83bf7f6","external_id":"abb8d90e-7d43-41be-9dae-ad5e692240f5","ibn":null,"question_id":"55cfaf22","program":"SAT","module":"math","domain_code":"Q","domain":"Problem-Solving and Data Analysis","skill_code":"Q.C.","skill":"One-variable data: Distributions and measures of center and spread","difficulty":"E","score_band":2,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Data set X: 5 , 9 , 9 , 13 Data set Y: 5 , 9 , 9 , 13 , 27 The lists give the values in data sets X and Y. Which statement correctly compares the mean of data set X and the mean of data set Y?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: center;\">Data set X: <math alttext=\"5\"><mn>5</mn>\n</math>, <math alttext=\"9\"><mn>9</mn>\n</math>, <math alttext=\"9\"><mn>9</mn>\n</math>, <math alttext=\"13\"><mn>13</mn>\n</math></p>\n<p style=\"text-align: center;\">Data set Y: <math alttext=\"5\"><mn>5</mn>\n</math>, <math alttext=\"9\"><mn>9</mn>\n</math>, <math alttext=\"9\"><mn>9</mn>\n</math>, <math alttext=\"13\"><mn>13</mn>\n</math>, <math alttext=\"27\"><mn>27</mn>\n</math></p>\n<p>The lists give the values in data sets X and Y. Which statement correctly compares the mean of data set X and the mean of data set Y?</p>","rationale_html":"<p style=\"text-align: left;\">Choice B is correct. ​​The mean of a data set is the sum of the values in the data set divided by the number of values in the data set. It follows that the mean of data set X is <math alttext=\"StartFraction 5 plus 9 plus 9 plus 13 Over 4 EndFraction\"><mfrac><mrow><mn>5</mn><mo>+</mo><mn>9</mn><mo>+</mo><mn>9</mn><mo>+</mo><mn>13</mn></mrow><mn>4</mn></mfrac></math>, or <math alttext=\"9\"><mn>9</mn>\n</math>, and the mean of data set Y is&nbsp;<math alttext=\"StartFraction 5 plus 9 plus 9 plus 13 plus 27 Over 5 EndFraction\"><mfrac><mrow><mn>5</mn><mo>+</mo><mn>9</mn><mo>+</mo><mn>9</mn><mo>+</mo><mn>13</mn><mo>+</mo><mn>27</mn></mrow><mn>5</mn></mfrac></math>, or <math alttext=\"12.6\"><mn>12.6</mn>\n</math>. Since <math alttext=\"9\"><mn>9</mn>\n</math> is less than <math alttext=\"12.6\"><mn>12.6</mn>\n</math>, the mean of data set X is less than the mean of data set Y.</p>\n<p style=\"text-align: left;\">Alternate approach: Data set Y consists of the <math alttext=\"4\"><mn>4</mn>\n</math> values in data set X and one additional value, <math alttext=\"27\"><mn>27</mn>\n</math>. Since the additional value, <math alttext=\"27\"><mn>27</mn>\n</math>, is larger than any value in data set X, the mean of data set X is less than the mean of data set Y.</p>\n<p style=\"text-align: left;\">Choice A is incorrect and may result from conceptual or calculation errors.</p>\n<p style=\"text-align: left;\">Choice C is incorrect and may result from conceptual or calculation errors.</p>\n<p style=\"text-align: left;\">Choice D is incorrect and may result from conceptual or calculation errors.</p>","correct_answer":["B"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.833000+00:00","source_updated_at":"2023-08-02T20:25:59.833000+00:00","options":[{"label":"A","content_html":"<p>The mean of data set X is greater than the mean of data set Y.</p>","ord":0},{"label":"B","content_html":"<p>The mean of data set X is less than the mean of data set Y.</p>","ord":1},{"label":"C","content_html":"<p>The means of data set X and data set Y are equal.</p>","ord":2},{"label":"D","content_html":"<p>There is not enough information to compare the means.</p>","ord":3}],"attribution":{"source_id":"cb_question_bank","source_name":"College Board digital SAT question bank (community dump)","rights_holder":"College Board","canonical_url":"https://satsuitequestionbank.collegeboard.org/","retrieved_from":"https://raw.githubusercontent.com/mdn522/sat-question-bank/main/data/cb-digital-questions.json","attribution":"SAT practice questions © College Board, from the official SAT Suite Question Bank. Retrieved via the community dump at github.com/mdn522/sat-question-bank.","disclaimer":"SAT® and PSAT/NMSQT® are trademarks registered by the College Board, which is not affiliated with, does not sponsor, and does not endorse this project.","license":"College Board copyright; source repository carries no licence. Local use only.","redistributable":false,"item_count":2017}}